Rockfish Historical Harvest Estimates

Summary

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}) \end{equation}\].

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: HR_fitLBR_2bias_hierPcomp_3pH_CLEAN_thru2023_5e+06_7kn_2025-04-24 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9972

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 12.- Residuals from logbook harvests

SWHS residuals

Figure 13.- Residuals from SWHS harvests.

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 15.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta1_pH 2 1.264104 beta2_pH 1 1.257358

parameter n badRhat_avg beta1_black 1 1.127744 beta2_pelagic 1 1.123629

Table 2. Summary of unconverged parameters by area

	NSEI	PWSI	PWSO	WKMA
beta1_black	1	0	0	0
beta1_pH	0	1	1	0
beta2_pelagic	0	0	1	0
beta2_pH	0	0	0	1

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.121	0.075	-0.256	-0.124	0.039
mu_bc_H[2]	-0.095	0.046	-0.172	-0.100	0.005
mu_bc_H[3]	-0.432	0.072	-0.571	-0.434	-0.283
mu_bc_H[4]	-0.983	0.190	-1.357	-0.983	-0.618
mu_bc_H[5]	0.952	1.118	-0.194	0.741	3.432
mu_bc_H[6]	-2.154	0.319	-2.778	-2.159	-1.499
mu_bc_H[7]	-0.457	0.109	-0.672	-0.453	-0.252
mu_bc_H[8]	0.239	0.370	-0.366	0.203	1.091
mu_bc_H[9]	-0.295	0.135	-0.556	-0.298	-0.025
mu_bc_H[10]	-0.108	0.069	-0.236	-0.110	0.034
mu_bc_H[11]	-0.125	0.037	-0.200	-0.125	-0.051
mu_bc_H[12]	-0.254	0.107	-0.483	-0.252	-0.049
mu_bc_H[13]	-0.134	0.079	-0.284	-0.135	0.024
mu_bc_H[14]	-0.301	0.097	-0.504	-0.299	-0.111
mu_bc_H[15]	-0.341	0.049	-0.437	-0.342	-0.239
mu_bc_H[16]	-0.255	0.374	-0.881	-0.285	0.549
mu_bc_R[1]	1.348	0.148	1.061	1.345	1.639
mu_bc_R[2]	1.455	0.093	1.264	1.455	1.640
mu_bc_R[3]	1.408	0.148	1.111	1.411	1.690
mu_bc_R[4]	0.898	0.205	0.468	0.906	1.272
mu_bc_R[5]	1.164	0.471	0.232	1.169	2.097
mu_bc_R[6]	-1.607	0.419	-2.459	-1.610	-0.778
mu_bc_R[7]	0.458	0.213	0.025	0.461	0.856
mu_bc_R[8]	0.546	0.199	0.151	0.552	0.927
mu_bc_R[9]	0.350	0.207	-0.087	0.365	0.714
mu_bc_R[10]	1.291	0.140	1.005	1.295	1.552
mu_bc_R[11]	1.040	0.096	0.852	1.044	1.222
mu_bc_R[12]	0.823	0.200	0.422	0.828	1.206
mu_bc_R[13]	1.029	0.103	0.820	1.030	1.223
mu_bc_R[14]	0.896	0.140	0.620	0.898	1.166
mu_bc_R[15]	0.780	0.110	0.572	0.779	0.998
mu_bc_R[16]	1.095	0.126	0.840	1.096	1.341
tau_pH[1]	5.145	0.437	4.331	5.132	6.037
tau_pH[2]	1.985	0.223	1.576	1.980	2.452
tau_pH[3]	2.131	0.222	1.710	2.120	2.595
beta0_pH[1,1]	0.578	0.174	0.220	0.578	0.907
beta0_pH[2,1]	1.378	0.173	1.024	1.382	1.703
beta0_pH[3,1]	1.429	0.188	1.019	1.440	1.768
beta0_pH[4,1]	1.575	0.214	1.105	1.595	1.947
beta0_pH[5,1]	-0.871	0.286	-1.477	-0.852	-0.390
beta0_pH[6,1]	-0.719	0.428	-1.780	-0.652	-0.085
beta0_pH[7,1]	-0.524	0.496	-1.666	-0.489	0.414
beta0_pH[8,1]	-0.664	0.275	-1.277	-0.634	-0.211
beta0_pH[9,1]	-0.656	0.274	-1.253	-0.635	-0.165
beta0_pH[10,1]	0.233	0.201	-0.176	0.240	0.617
beta0_pH[11,1]	-0.090	0.172	-0.444	-0.082	0.233
beta0_pH[12,1]	0.489	0.190	0.104	0.489	0.836
beta0_pH[13,1]	0.005	0.146	-0.292	0.009	0.287
beta0_pH[14,1]	-0.313	0.168	-0.652	-0.308	0.011
beta0_pH[15,1]	-0.029	0.176	-0.370	-0.027	0.311
beta0_pH[16,1]	-0.471	0.359	-1.341	-0.418	0.060
beta0_pH[1,2]	2.810	0.169	2.464	2.813	3.133
beta0_pH[2,2]	2.880	0.137	2.615	2.876	3.148
beta0_pH[3,2]	3.133	0.150	2.852	3.125	3.439
beta0_pH[4,2]	2.951	0.133	2.695	2.952	3.222
beta0_pH[5,2]	4.830	1.417	2.999	4.529	8.245
beta0_pH[6,2]	3.112	0.213	2.699	3.109	3.537
beta0_pH[7,2]	1.830	0.201	1.416	1.835	2.203
beta0_pH[8,2]	2.878	0.176	2.544	2.877	3.222
beta0_pH[9,2]	3.441	0.221	3.014	3.434	3.887
beta0_pH[10,2]	3.757	0.199	3.381	3.750	4.153
beta0_pH[11,2]	-4.848	0.306	-5.431	-4.848	-4.249
beta0_pH[12,2]	-4.759	0.390	-5.537	-4.748	-4.019
beta0_pH[13,2]	-4.564	0.402	-5.350	-4.579	-3.756
beta0_pH[14,2]	-5.586	0.469	-6.550	-5.574	-4.727
beta0_pH[15,2]	-4.292	0.344	-4.928	-4.298	-3.591
beta0_pH[16,2]	-4.859	0.397	-5.679	-4.847	-4.094
beta0_pH[1,3]	0.101	0.671	-1.433	0.194	1.170
beta0_pH[2,3]	2.195	0.158	1.885	2.200	2.489
beta0_pH[3,3]	2.528	0.152	2.228	2.528	2.828
beta0_pH[4,3]	2.972	0.161	2.653	2.973	3.281
beta0_pH[5,3]	2.096	1.380	0.362	1.822	5.424
beta0_pH[6,3]	0.991	0.515	-0.271	1.026	1.881
beta0_pH[7,3]	0.630	0.172	0.304	0.627	0.980
beta0_pH[8,3]	0.308	0.191	-0.068	0.310	0.674
beta0_pH[9,3]	-0.630	0.383	-1.646	-0.600	0.025
beta0_pH[10,3]	0.478	0.377	-0.438	0.530	1.083
beta0_pH[11,3]	-0.149	0.312	-0.746	-0.152	0.483
beta0_pH[12,3]	-0.833	0.358	-1.601	-0.806	-0.203
beta0_pH[13,3]	-0.116	0.305	-0.712	-0.118	0.487
beta0_pH[14,3]	-0.269	0.263	-0.782	-0.267	0.259
beta0_pH[15,3]	-0.685	0.319	-1.357	-0.675	-0.118
beta0_pH[16,3]	-0.382	0.288	-0.934	-0.378	0.189
beta1_pH[1,1]	3.023	0.324	2.463	3.003	3.737
beta1_pH[2,1]	2.144	0.281	1.644	2.126	2.752
beta1_pH[3,1]	1.957	0.292	1.447	1.937	2.604
beta1_pH[4,1]	2.377	0.352	1.833	2.337	3.205
beta1_pH[5,1]	2.310	0.361	1.723	2.280	3.107
beta1_pH[6,1]	3.842	1.074	2.371	3.613	6.502
beta1_pH[7,1]	2.649	0.969	0.943	2.558	4.915
beta1_pH[8,1]	4.002	0.942	2.625	3.836	6.359
beta1_pH[9,1]	2.336	0.376	1.696	2.296	3.193
beta1_pH[10,1]	2.399	0.280	1.887	2.386	2.993
beta1_pH[11,1]	3.268	0.213	2.860	3.262	3.708
beta1_pH[12,1]	2.548	0.223	2.124	2.544	2.997
beta1_pH[13,1]	2.967	0.214	2.558	2.958	3.425
beta1_pH[14,1]	3.417	0.221	2.998	3.414	3.863
beta1_pH[15,1]	2.530	0.220	2.101	2.528	2.958
beta1_pH[16,1]	4.092	0.642	3.163	3.975	5.589
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.000	0.010	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.005	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.691	0.339	6.019	6.694	7.325
beta1_pH[12,2]	6.415	0.451	5.608	6.403	7.331
beta1_pH[13,2]	6.940	0.444	6.075	6.938	7.811
beta1_pH[14,2]	7.222	0.490	6.306	7.208	8.222
beta1_pH[15,2]	6.771	0.380	6.026	6.766	7.513
beta1_pH[16,2]	7.451	0.438	6.626	7.435	8.337
beta1_pH[1,3]	4.150	1.568	1.808	3.902	7.659
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.835	6.465	0.812	2.788	14.686
beta1_pH[6,3]	3.248	4.326	0.390	2.645	11.292
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.744	0.352	2.068	2.739	3.447
beta1_pH[9,3]	2.752	0.449	1.996	2.716	3.798
beta1_pH[10,3]	2.901	0.460	2.162	2.846	4.012
beta1_pH[11,3]	2.729	0.375	2.018	2.716	3.504
beta1_pH[12,3]	4.089	0.453	3.249	4.064	5.051
beta1_pH[13,3]	1.698	0.331	1.047	1.703	2.356
beta1_pH[14,3]	2.515	0.336	1.864	2.512	3.178
beta1_pH[15,3]	1.969	0.346	1.331	1.955	2.676
beta1_pH[16,3]	1.788	0.319	1.151	1.793	2.427
beta2_pH[1,1]	0.489	0.128	0.292	0.474	0.794
beta2_pH[2,1]	0.586	0.318	0.244	0.526	1.329
beta2_pH[3,1]	0.669	0.476	0.242	0.572	1.708
beta2_pH[4,1]	0.487	0.206	0.212	0.459	0.933
beta2_pH[5,1]	1.481	0.981	0.241	1.339	3.818
beta2_pH[6,1]	0.185	0.065	0.091	0.175	0.332
beta2_pH[7,1]	0.047	0.312	0.000	0.000	0.244
beta2_pH[8,1]	0.245	0.092	0.127	0.228	0.459
beta2_pH[9,1]	0.438	0.249	0.184	0.392	0.934
beta2_pH[10,1]	0.613	0.267	0.284	0.559	1.283
beta2_pH[11,1]	0.783	0.204	0.482	0.755	1.260
beta2_pH[12,1]	1.335	0.478	0.731	1.242	2.482
beta2_pH[13,1]	0.736	0.220	0.408	0.704	1.232
beta2_pH[14,1]	0.835	0.209	0.519	0.801	1.344
beta2_pH[15,1]	0.800	0.289	0.409	0.748	1.509
beta2_pH[16,1]	0.385	0.174	0.175	0.337	0.827
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-1.967	1.817	-6.695	-1.471	-0.034
beta2_pH[4,2]	-2.000	1.850	-6.800	-1.494	-0.031
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.589	4.556	-21.261	-8.407	-3.940
beta2_pH[12,2]	-8.272	5.251	-21.397	-7.332	-0.997
beta2_pH[13,2]	-8.158	5.199	-21.394	-7.094	-1.704
beta2_pH[14,2]	-8.757	4.906	-21.471	-7.574	-2.533
beta2_pH[15,2]	-9.482	4.677	-21.743	-8.413	-3.653
beta2_pH[16,2]	-9.709	4.565	-21.708	-8.711	-4.075
beta2_pH[1,3]	0.271	0.452	0.101	0.190	0.755
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	9.219	6.402	-0.075	8.384	24.493
beta2_pH[6,3]	9.287	6.435	0.237	8.168	24.306
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	10.078	5.815	1.858	8.847	24.358
beta2_pH[9,3]	9.042	6.348	0.512	8.030	23.926
beta2_pH[10,3]	8.735	6.527	0.490	7.745	24.096
beta2_pH[11,3]	-2.359	2.247	-8.736	-1.715	-0.611
beta2_pH[12,3]	-2.508	2.224	-8.702	-1.872	-0.943
beta2_pH[13,3]	-2.996	2.534	-9.874	-2.179	-0.771
beta2_pH[14,3]	-2.946	2.575	-10.390	-2.119	-0.860
beta2_pH[15,3]	-3.077	2.598	-10.432	-2.244	-0.972
beta2_pH[16,3]	-3.125	2.655	-10.853	-2.237	-0.877
beta3_pH[1,1]	35.928	0.841	34.341	35.894	37.651
beta3_pH[2,1]	33.624	1.215	31.553	33.529	36.370
beta3_pH[3,1]	33.620	1.020	31.639	33.597	35.768
beta3_pH[4,1]	33.856	1.190	31.688	33.795	36.367
beta3_pH[5,1]	27.666	1.039	26.502	27.469	30.647
beta3_pH[6,1]	38.297	3.138	32.453	38.077	44.929
beta3_pH[7,1]	30.697	8.043	18.626	30.076	45.149
beta3_pH[8,1]	39.941	2.083	36.273	39.715	44.735
beta3_pH[9,1]	30.653	1.464	28.067	30.528	33.858
beta3_pH[10,1]	32.733	0.915	31.027	32.711	34.625
beta3_pH[11,1]	30.315	0.468	29.401	30.324	31.230
beta3_pH[12,1]	30.162	0.401	29.369	30.175	30.930
beta3_pH[13,1]	33.175	0.576	32.076	33.166	34.352
beta3_pH[14,1]	32.034	0.469	31.143	32.016	32.983
beta3_pH[15,1]	31.193	0.656	29.930	31.186	32.536
beta3_pH[16,1]	32.003	1.033	30.315	31.890	34.366
beta3_pH[1,2]	30.042	7.934	18.525	29.266	44.728
beta3_pH[2,2]	30.087	7.957	18.488	29.246	44.852
beta3_pH[3,2]	30.033	7.998	18.495	28.898	44.975
beta3_pH[4,2]	29.806	7.918	18.412	28.571	44.811
beta3_pH[5,2]	29.880	8.070	18.427	28.848	44.937
beta3_pH[6,2]	29.899	7.957	18.427	28.892	44.695
beta3_pH[7,2]	29.980	7.966	18.340	29.032	44.763
beta3_pH[8,2]	29.794	7.842	18.559	28.672	44.950
beta3_pH[9,2]	30.032	8.038	18.434	29.232	44.859
beta3_pH[10,2]	30.192	7.999	18.482	29.155	44.965
beta3_pH[11,2]	43.407	0.179	43.115	43.390	43.774
beta3_pH[12,2]	43.185	0.184	42.944	43.138	43.675
beta3_pH[13,2]	43.866	0.152	43.449	43.910	44.043
beta3_pH[14,2]	43.305	0.212	43.045	43.244	43.815
beta3_pH[15,2]	43.408	0.191	43.101	43.389	43.797
beta3_pH[16,2]	43.497	0.187	43.164	43.489	43.850
beta3_pH[1,3]	39.330	3.224	32.864	39.342	45.392
beta3_pH[2,3]	30.164	8.047	18.413	29.246	44.960
beta3_pH[3,3]	30.526	8.035	18.496	29.906	45.125
beta3_pH[4,3]	30.465	8.034	18.535	29.817	44.928
beta3_pH[5,3]	36.709	3.798	31.225	36.137	44.956
beta3_pH[6,3]	40.398	3.598	31.537	40.800	45.675
beta3_pH[7,3]	38.046	4.298	31.312	37.999	45.501
beta3_pH[8,3]	41.504	0.255	41.074	41.510	41.942
beta3_pH[9,3]	33.464	0.585	31.646	33.550	34.327
beta3_pH[10,3]	35.845	0.778	33.560	36.023	36.849
beta3_pH[11,3]	41.788	0.818	40.118	41.838	43.272
beta3_pH[12,3]	41.715	0.389	40.959	41.725	42.489
beta3_pH[13,3]	42.731	0.873	41.014	42.761	44.599
beta3_pH[14,3]	41.104	0.573	39.883	41.125	42.139
beta3_pH[15,3]	42.620	0.681	41.175	42.692	43.792
beta3_pH[16,3]	42.883	0.737	41.203	42.991	44.132
beta0_pelagic[1]	2.223	0.134	1.958	2.224	2.483
beta0_pelagic[2]	1.518	0.127	1.268	1.518	1.770
beta0_pelagic[3]	-0.409	0.696	-1.999	-0.283	0.579
beta0_pelagic[4]	-0.314	0.776	-2.107	-0.154	0.787
beta0_pelagic[5]	1.192	0.246	0.686	1.199	1.663
beta0_pelagic[6]	1.465	0.268	0.880	1.481	1.976
beta0_pelagic[7]	1.593	0.210	1.197	1.586	2.052
beta0_pelagic[8]	1.757	0.206	1.367	1.750	2.199
beta0_pelagic[9]	2.477	0.312	1.879	2.488	3.028
beta0_pelagic[10]	2.531	0.198	2.106	2.534	2.923
beta0_pelagic[11]	-0.018	0.524	-1.211	0.026	0.689
beta0_pelagic[12]	1.680	0.142	1.405	1.683	1.953
beta0_pelagic[13]	0.297	0.219	-0.220	0.321	0.659
beta0_pelagic[14]	-0.102	0.278	-0.729	-0.083	0.372
beta0_pelagic[15]	-0.265	0.143	-0.553	-0.265	0.009
beta0_pelagic[16]	0.273	0.301	-0.506	0.346	0.675
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	1.943	1.077	0.486	1.754	4.482
beta1_pelagic[4]	1.728	1.034	0.419	1.472	4.374
beta1_pelagic[5]	-0.074	0.307	-0.678	-0.074	0.525
beta1_pelagic[6]	-0.100	0.447	-0.869	-0.139	0.745
beta1_pelagic[7]	-0.016	0.291	-0.584	-0.020	0.545
beta1_pelagic[8]	-0.007	0.284	-0.558	-0.005	0.553
beta1_pelagic[9]	0.203	0.487	-0.748	0.309	0.968
beta1_pelagic[10]	0.069	0.258	-0.442	0.068	0.586
beta1_pelagic[11]	3.925	1.282	2.166	3.798	6.559
beta1_pelagic[12]	2.785	0.314	2.211	2.776	3.427
beta1_pelagic[13]	2.963	0.773	1.778	2.832	4.745
beta1_pelagic[14]	4.320	1.000	2.780	4.165	6.599
beta1_pelagic[15]	2.912	0.266	2.413	2.901	3.456
beta1_pelagic[16]	3.681	0.992	2.678	3.308	6.483
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.679	2.150	0.037	0.150	6.471
beta2_pelagic[4]	1.159	2.789	0.033	0.354	10.504
beta2_pelagic[5]	-0.032	0.680	-1.476	-0.020	1.385
beta2_pelagic[6]	-0.100	0.695	-1.483	-0.157	1.343
beta2_pelagic[7]	-0.005	0.649	-1.404	0.003	1.368
beta2_pelagic[8]	0.016	0.633	-1.306	0.004	1.344
beta2_pelagic[9]	0.190	0.670	-1.239	0.252	1.448
beta2_pelagic[10]	0.034	0.619	-1.266	0.019	1.319
beta2_pelagic[11]	1.686	3.840	0.100	0.232	12.416
beta2_pelagic[12]	5.945	4.944	1.009	4.512	19.682
beta2_pelagic[13]	0.921	2.031	0.180	0.463	5.254
beta2_pelagic[14]	0.326	0.211	0.160	0.290	0.664
beta2_pelagic[15]	6.084	4.799	1.237	4.786	19.405
beta2_pelagic[16]	4.595	5.240	0.186	3.021	18.370
beta3_pelagic[1]	29.717	7.916	18.473	28.574	45.009
beta3_pelagic[2]	29.663	7.896	18.439	28.461	44.766
beta3_pelagic[3]	29.455	6.435	18.941	28.915	43.800
beta3_pelagic[4]	25.031	4.825	18.725	24.221	39.022
beta3_pelagic[5]	30.055	8.147	18.469	28.691	45.258
beta3_pelagic[6]	31.671	6.817	18.924	31.594	44.561
beta3_pelagic[7]	29.564	7.912	18.455	28.336	44.969
beta3_pelagic[8]	29.347	8.060	18.378	27.805	44.990
beta3_pelagic[9]	30.816	6.010	19.215	30.865	42.426
beta3_pelagic[10]	29.806	8.224	18.486	28.446	45.278
beta3_pelagic[11]	42.586	1.872	37.896	43.034	45.635
beta3_pelagic[12]	43.468	0.286	42.994	43.457	43.997
beta3_pelagic[13]	42.798	1.362	40.285	42.730	45.611
beta3_pelagic[14]	42.324	1.665	39.027	42.344	45.547
beta3_pelagic[15]	43.164	0.269	42.499	43.171	43.655
beta3_pelagic[16]	43.148	0.835	41.029	43.235	44.981
mu_beta0_pelagic[1]	0.671	1.048	-1.640	0.752	2.567
mu_beta0_pelagic[2]	1.821	0.385	1.031	1.823	2.611
mu_beta0_pelagic[3]	0.310	0.465	-0.664	0.322	1.192
tau_beta0_pelagic[1]	0.483	0.548	0.051	0.302	2.011
tau_beta0_pelagic[2]	2.727	2.911	0.261	1.942	9.258
tau_beta0_pelagic[3]	1.545	1.214	0.169	1.250	4.779
beta0_yellow[1]	-0.525	0.188	-0.931	-0.507	-0.219
beta0_yellow[2]	0.501	0.168	0.153	0.512	0.788
beta0_yellow[3]	-0.320	0.192	-0.724	-0.313	0.017
beta0_yellow[4]	0.848	0.282	0.117	0.894	1.224
beta0_yellow[5]	-0.294	0.349	-0.976	-0.293	0.399
beta0_yellow[6]	1.115	0.165	0.790	1.113	1.440
beta0_yellow[7]	0.985	0.161	0.680	0.981	1.302
beta0_yellow[8]	1.015	0.157	0.702	1.014	1.327
beta0_yellow[9]	0.663	0.160	0.344	0.664	0.973
beta0_yellow[10]	0.580	0.142	0.304	0.581	0.859
beta0_yellow[11]	-1.971	0.467	-2.866	-1.972	-1.016
beta0_yellow[12]	-3.675	0.413	-4.546	-3.646	-2.913
beta0_yellow[13]	-3.707	0.457	-4.670	-3.688	-2.871
beta0_yellow[14]	-2.099	0.566	-3.070	-2.141	-0.650
beta0_yellow[15]	-2.855	0.414	-3.660	-2.844	-2.043
beta0_yellow[16]	-2.430	0.461	-3.307	-2.435	-1.506
beta1_yellow[1]	0.914	1.205	0.016	0.722	2.986
beta1_yellow[2]	1.075	0.374	0.604	1.024	1.931
beta1_yellow[3]	0.719	0.278	0.228	0.702	1.344
beta1_yellow[4]	1.347	0.729	0.662	1.162	3.574
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.113	0.466	1.160	2.116	2.998
beta1_yellow[12]	2.468	0.427	1.662	2.437	3.384
beta1_yellow[13]	2.824	0.459	1.989	2.808	3.788
beta1_yellow[14]	2.178	0.544	0.913	2.207	3.170
beta1_yellow[15]	2.104	0.412	1.313	2.092	2.932
beta1_yellow[16]	2.186	0.464	1.227	2.198	3.087
beta2_yellow[1]	-3.839	3.242	-11.920	-3.045	-0.078
beta2_yellow[2]	-3.944	3.221	-11.886	-3.114	-0.193
beta2_yellow[3]	-3.950	3.265	-11.711	-3.076	-0.159
beta2_yellow[4]	-3.551	3.464	-12.062	-2.521	-0.099
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.668	2.688	-11.300	-4.114	-1.061
beta2_yellow[12]	-5.049	2.663	-11.833	-4.470	-1.383
beta2_yellow[13]	-4.939	2.653	-11.696	-4.314	-1.541
beta2_yellow[14]	-4.856	2.901	-11.755	-4.307	-0.449
beta2_yellow[15]	-4.377	2.707	-11.301	-3.726	-1.026
beta2_yellow[16]	-5.059	2.732	-12.070	-4.520	-1.440
beta3_yellow[1]	25.326	6.782	18.295	22.318	43.484
beta3_yellow[2]	29.076	1.855	25.269	28.892	32.627
beta3_yellow[3]	32.977	2.994	26.355	32.892	39.693
beta3_yellow[4]	28.989	3.447	22.324	27.899	35.995
beta3_yellow[5]	30.163	7.912	18.520	29.250	44.943
beta3_yellow[6]	30.000	8.032	18.435	28.949	45.015
beta3_yellow[7]	30.195	7.740	18.463	29.485	44.846
beta3_yellow[8]	29.860	7.943	18.425	28.758	44.868
beta3_yellow[9]	30.223	8.033	18.472	29.289	44.996
beta3_yellow[10]	30.059	7.904	18.517	29.058	44.691
beta3_yellow[11]	45.297	0.554	44.006	45.398	45.973
beta3_yellow[12]	43.297	0.379	42.529	43.275	44.055
beta3_yellow[13]	44.867	0.389	44.021	44.939	45.557
beta3_yellow[14]	44.031	1.748	36.810	44.229	45.828
beta3_yellow[15]	45.168	0.540	44.108	45.152	45.976
beta3_yellow[16]	44.562	0.671	43.356	44.559	45.852
mu_beta0_yellow[1]	0.107	0.544	-1.074	0.102	1.216
mu_beta0_yellow[2]	0.634	0.332	-0.103	0.649	1.273
mu_beta0_yellow[3]	-2.456	0.645	-3.469	-2.548	-0.874
tau_beta0_yellow[1]	1.829	2.508	0.088	1.175	6.823
tau_beta0_yellow[2]	3.439	3.943	0.328	2.357	13.019
tau_beta0_yellow[3]	1.469	1.919	0.103	0.924	6.109
beta0_black[1]	-0.078	0.157	-0.384	-0.074	0.221
beta0_black[2]	1.914	0.129	1.664	1.916	2.167
beta0_black[3]	1.314	0.137	1.055	1.317	1.583
beta0_black[4]	2.428	0.132	2.170	2.430	2.686
beta0_black[5]	1.564	2.022	-3.079	1.662	5.745
beta0_black[6]	1.609	2.019	-2.944	1.667	5.797
beta0_black[7]	1.578	2.057	-2.872	1.635	5.907
beta0_black[8]	1.298	0.226	0.853	1.298	1.734
beta0_black[9]	2.452	0.253	1.971	2.451	2.945
beta0_black[10]	1.476	0.135	1.209	1.479	1.734
beta0_black[11]	3.487	0.153	3.182	3.487	3.784
beta0_black[12]	4.877	0.175	4.535	4.875	5.220
beta0_black[13]	-0.150	0.314	-0.720	-0.127	0.326
beta0_black[14]	2.856	0.161	2.559	2.855	3.176
beta0_black[15]	1.289	0.158	0.981	1.285	1.599
beta0_black[16]	4.275	0.164	3.963	4.273	4.590
beta2_black[1]	7.989	10.063	0.527	3.600	39.253
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.789	1.579	-6.304	-1.279	-0.260
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.777	1.029	39.914	41.933	43.248
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.127	1.172	36.954	39.287	40.693
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.261	0.198	-0.658	-0.261	0.129
beta4_black[2]	0.244	0.182	-0.109	0.246	0.611
beta4_black[3]	-0.929	0.200	-1.321	-0.922	-0.548
beta4_black[4]	0.425	0.214	0.015	0.420	0.840
beta4_black[5]	0.187	2.487	-4.480	0.123	4.932
beta4_black[6]	0.227	2.596	-4.516	0.128	4.887
beta4_black[7]	0.162	2.593	-4.753	0.128	4.693
beta4_black[8]	-0.699	0.376	-1.425	-0.692	0.034
beta4_black[9]	1.456	1.021	-0.153	1.320	3.811
beta4_black[10]	0.024	0.192	-0.355	0.024	0.401
beta4_black[11]	-0.700	0.214	-1.133	-0.699	-0.274
beta4_black[12]	0.170	0.330	-0.466	0.160	0.816
beta4_black[13]	-1.185	0.226	-1.615	-1.183	-0.735
beta4_black[14]	-0.182	0.236	-0.640	-0.178	0.283
beta4_black[15]	-0.880	0.214	-1.303	-0.878	-0.460
beta4_black[16]	-0.596	0.232	-1.046	-0.601	-0.123
mu_beta0_black[1]	1.277	0.914	-0.790	1.307	3.083
mu_beta0_black[2]	1.587	0.953	-0.728	1.686	3.388
mu_beta0_black[3]	2.530	0.973	0.426	2.572	4.386
tau_beta0_black[1]	0.627	0.583	0.060	0.448	2.235
tau_beta0_black[2]	1.856	3.460	0.057	0.804	9.769
tau_beta0_black[3]	0.235	0.151	0.052	0.201	0.619
beta0_dsr[11]	-2.897	0.292	-3.484	-2.889	-2.353
beta0_dsr[12]	4.554	0.295	4.002	4.552	5.126
beta0_dsr[13]	-1.368	0.371	-1.984	-1.340	-0.798
beta0_dsr[14]	-3.692	0.508	-4.714	-3.676	-2.719
beta0_dsr[15]	-1.947	0.283	-2.506	-1.948	-1.397
beta0_dsr[16]	-2.989	0.355	-3.703	-2.977	-2.324
beta1_dsr[11]	4.835	0.309	4.249	4.828	5.437
beta1_dsr[12]	6.904	13.336	2.231	5.029	18.599
beta1_dsr[13]	2.889	0.466	2.295	2.853	3.575
beta1_dsr[14]	6.357	0.533	5.353	6.350	7.419
beta1_dsr[15]	3.343	0.285	2.785	3.335	3.915
beta1_dsr[16]	5.808	0.370	5.103	5.806	6.536
beta2_dsr[11]	-8.214	2.345	-13.812	-7.836	-4.699
beta2_dsr[12]	-7.123	2.713	-13.150	-6.929	-2.484
beta2_dsr[13]	-6.477	2.781	-12.317	-6.366	-1.180
beta2_dsr[14]	-6.203	2.703	-12.146	-6.087	-1.840
beta2_dsr[15]	-7.757	2.418	-13.320	-7.471	-3.810
beta2_dsr[16]	-7.909	2.388	-13.370	-7.571	-4.184
beta3_dsr[11]	43.490	0.152	43.211	43.485	43.783
beta3_dsr[12]	33.979	0.761	32.138	34.125	34.830
beta3_dsr[13]	43.262	0.342	42.787	43.198	43.882
beta3_dsr[14]	43.347	0.233	43.079	43.277	43.940
beta3_dsr[15]	43.502	0.188	43.160	43.501	43.852
beta3_dsr[16]	43.439	0.159	43.175	43.423	43.763
beta4_dsr[11]	0.587	0.218	0.172	0.586	1.014
beta4_dsr[12]	0.253	0.446	-0.624	0.252	1.193
beta4_dsr[13]	-0.166	0.224	-0.606	-0.160	0.264
beta4_dsr[14]	0.146	0.257	-0.358	0.147	0.646
beta4_dsr[15]	0.723	0.220	0.306	0.715	1.155
beta4_dsr[16]	0.153	0.226	-0.293	0.159	0.588
beta0_slope[11]	-1.841	0.147	-2.131	-1.838	-1.549
beta0_slope[12]	-4.464	0.259	-4.988	-4.456	-3.976
beta0_slope[13]	-1.345	0.180	-1.733	-1.326	-1.044
beta0_slope[14]	-2.670	0.167	-2.997	-2.671	-2.346
beta0_slope[15]	-1.341	0.148	-1.627	-1.342	-1.047
beta0_slope[16]	-2.737	0.156	-3.038	-2.736	-2.420
beta1_slope[11]	4.491	0.220	4.060	4.487	4.923
beta1_slope[12]	3.983	0.437	3.114	3.984	4.824
beta1_slope[13]	2.719	0.435	2.197	2.652	4.038
beta1_slope[14]	6.331	0.409	5.549	6.322	7.149
beta1_slope[15]	3.005	0.205	2.591	3.005	3.395
beta1_slope[16]	5.287	0.283	4.744	5.290	5.837
beta2_slope[11]	8.617	2.261	5.065	8.277	13.805
beta2_slope[12]	6.608	2.867	1.248	6.638	12.325
beta2_slope[13]	5.372	3.032	0.422	5.358	11.591
beta2_slope[14]	6.368	2.579	2.213	6.237	12.093
beta2_slope[15]	8.182	2.324	4.547	7.882	13.613
beta2_slope[16]	7.738	2.275	4.219	7.459	13.148
beta3_slope[11]	43.459	0.135	43.219	43.452	43.734
beta3_slope[12]	43.348	0.271	42.866	43.311	43.886
beta3_slope[13]	43.455	0.384	42.940	43.398	44.063
beta3_slope[14]	43.270	0.139	43.094	43.235	43.627
beta3_slope[15]	43.490	0.163	43.195	43.488	43.797
beta3_slope[16]	43.377	0.144	43.152	43.356	43.694
beta4_slope[11]	-0.735	0.163	-1.068	-0.733	-0.425
beta4_slope[12]	-1.164	0.464	-2.140	-1.130	-0.341
beta4_slope[13]	0.087	0.163	-0.237	0.086	0.393
beta4_slope[14]	-0.092	0.201	-0.480	-0.098	0.295
beta4_slope[15]	-0.766	0.163	-1.094	-0.762	-0.451
beta4_slope[16]	-0.164	0.177	-0.503	-0.164	0.180
sigma_H[1]	0.205	0.057	0.101	0.200	0.332
sigma_H[2]	0.171	0.030	0.118	0.169	0.234
sigma_H[3]	0.197	0.042	0.122	0.194	0.288
sigma_H[4]	0.422	0.077	0.297	0.413	0.603
sigma_H[5]	0.996	0.206	0.616	0.988	1.420
sigma_H[6]	0.394	0.202	0.035	0.392	0.810
sigma_H[7]	0.311	0.067	0.211	0.300	0.469
sigma_H[8]	0.416	0.085	0.273	0.407	0.596
sigma_H[9]	0.525	0.128	0.324	0.507	0.816
sigma_H[10]	0.214	0.042	0.140	0.211	0.307
sigma_H[11]	0.277	0.045	0.203	0.272	0.376
sigma_H[12]	0.431	0.163	0.203	0.402	0.771
sigma_H[13]	0.215	0.037	0.151	0.212	0.295
sigma_H[14]	0.511	0.094	0.349	0.505	0.705
sigma_H[15]	0.246	0.041	0.178	0.242	0.337
sigma_H[16]	0.224	0.044	0.153	0.220	0.324
lambda_H[1]	3.044	3.854	0.164	1.769	13.401
lambda_H[2]	8.396	7.865	0.772	6.061	30.194
lambda_H[3]	6.231	9.050	0.277	3.137	34.326
lambda_H[4]	0.006	0.004	0.001	0.005	0.016
lambda_H[5]	4.472	10.361	0.035	1.041	34.680
lambda_H[6]	7.660	14.106	0.008	0.971	46.170
lambda_H[7]	0.013	0.009	0.002	0.011	0.037
lambda_H[8]	8.462	10.628	0.120	4.784	37.394
lambda_H[9]	0.015	0.010	0.003	0.013	0.041
lambda_H[10]	0.297	0.410	0.034	0.203	1.113
lambda_H[11]	0.259	0.406	0.012	0.123	1.201
lambda_H[12]	4.822	6.199	0.189	2.729	22.560
lambda_H[13]	3.505	3.280	0.258	2.570	12.152
lambda_H[14]	3.407	4.550	0.204	2.029	14.986
lambda_H[15]	0.026	0.042	0.003	0.016	0.106
lambda_H[16]	0.847	1.176	0.040	0.433	4.147
mu_lambda_H[1]	4.356	1.898	1.268	4.136	8.496
mu_lambda_H[2]	3.898	1.971	0.723	3.725	8.102
mu_lambda_H[3]	3.507	1.819	0.771	3.237	7.659
sigma_lambda_H[1]	8.690	4.273	2.129	8.149	18.056
sigma_lambda_H[2]	8.483	4.665	1.217	7.798	18.445
sigma_lambda_H[3]	6.351	3.993	0.993	5.451	16.216
beta_H[1,1]	6.917	1.071	4.224	7.074	8.540
beta_H[2,1]	9.892	0.468	8.900	9.913	10.738
beta_H[3,1]	7.993	0.770	6.231	8.092	9.224
beta_H[4,1]	9.504	7.964	-6.568	9.723	24.623
beta_H[5,1]	0.185	2.261	-4.556	0.366	4.105
beta_H[6,1]	3.186	4.156	-7.297	4.682	7.814
beta_H[7,1]	0.511	5.864	-12.463	1.023	10.793
beta_H[8,1]	1.391	4.005	-2.409	1.225	3.552
beta_H[9,1]	13.060	5.650	1.890	13.020	23.995
beta_H[10,1]	7.120	1.673	3.685	7.199	10.412
beta_H[11,1]	5.077	3.490	-2.691	5.770	9.990
beta_H[12,1]	2.621	1.030	0.786	2.556	4.845
beta_H[13,1]	9.025	0.917	7.099	9.083	10.492
beta_H[14,1]	2.200	1.046	0.289	2.195	4.400
beta_H[15,1]	-6.183	3.876	-13.128	-6.423	2.389
beta_H[16,1]	3.441	2.632	-0.754	3.116	9.803
beta_H[1,2]	7.896	0.249	7.382	7.903	8.367
beta_H[2,2]	10.025	0.134	9.756	10.025	10.285
beta_H[3,2]	8.952	0.199	8.570	8.951	9.343
beta_H[4,2]	3.550	1.497	0.708	3.519	6.621
beta_H[5,2]	1.962	0.951	0.080	1.983	3.798
beta_H[6,2]	5.721	1.074	3.230	5.910	7.367
beta_H[7,2]	2.661	1.100	0.721	2.606	5.025
beta_H[8,2]	3.021	1.104	1.421	3.146	4.300
beta_H[9,2]	3.510	1.119	1.382	3.476	5.826
beta_H[10,2]	8.196	0.340	7.490	8.209	8.842
beta_H[11,2]	9.773	0.631	8.817	9.656	11.167
beta_H[12,2]	3.948	0.372	3.256	3.933	4.709
beta_H[13,2]	9.120	0.251	8.656	9.112	9.634
beta_H[14,2]	4.016	0.349	3.342	4.016	4.703
beta_H[15,2]	11.370	0.698	9.892	11.412	12.618
beta_H[16,2]	4.534	0.808	3.052	4.510	6.177
beta_H[1,3]	8.447	0.247	7.988	8.435	8.971
beta_H[2,3]	10.065	0.119	9.828	10.068	10.298
beta_H[3,3]	9.613	0.162	9.288	9.612	9.950
beta_H[4,3]	-2.517	0.882	-4.305	-2.519	-0.777
beta_H[5,3]	3.822	0.628	2.575	3.830	5.007
beta_H[6,3]	8.011	1.196	6.385	7.627	10.646
beta_H[7,3]	-2.780	0.654	-4.111	-2.774	-1.526
beta_H[8,3]	5.239	0.503	4.654	5.177	6.190
beta_H[9,3]	-2.843	0.745	-4.350	-2.841	-1.453
beta_H[10,3]	8.686	0.273	8.165	8.676	9.222
beta_H[11,3]	8.543	0.288	7.917	8.571	9.039
beta_H[12,3]	5.249	0.327	4.436	5.289	5.771
beta_H[13,3]	8.843	0.177	8.488	8.851	9.162
beta_H[14,3]	5.713	0.273	5.113	5.732	6.196
beta_H[15,3]	10.363	0.326	9.749	10.354	11.016
beta_H[16,3]	6.246	0.615	4.871	6.313	7.258
beta_H[1,4]	8.249	0.184	7.844	8.261	8.574
beta_H[2,4]	10.129	0.119	9.880	10.136	10.341
beta_H[3,4]	10.113	0.163	9.759	10.126	10.396
beta_H[4,4]	11.806	0.467	10.866	11.816	12.712
beta_H[5,4]	5.479	0.761	4.258	5.382	7.257
beta_H[6,4]	7.037	0.943	4.952	7.342	8.315
beta_H[7,4]	8.276	0.350	7.547	8.278	8.967
beta_H[8,4]	6.707	0.243	6.263	6.715	7.122
beta_H[9,4]	7.222	0.467	6.289	7.223	8.140
beta_H[10,4]	7.756	0.236	7.307	7.746	8.250
beta_H[11,4]	9.388	0.208	8.980	9.382	9.800
beta_H[12,4]	7.145	0.213	6.754	7.139	7.598
beta_H[13,4]	9.043	0.138	8.749	9.050	9.297
beta_H[14,4]	7.730	0.217	7.311	7.727	8.155
beta_H[15,4]	9.465	0.229	9.012	9.469	9.911
beta_H[16,4]	9.342	0.242	8.906	9.322	9.858
beta_H[1,5]	8.982	0.148	8.679	8.987	9.271
beta_H[2,5]	10.782	0.096	10.595	10.778	10.982
beta_H[3,5]	10.921	0.172	10.614	10.912	11.274
beta_H[4,5]	8.373	0.480	7.491	8.350	9.368
beta_H[5,5]	5.401	0.581	4.088	5.450	6.435
beta_H[6,5]	8.803	0.627	7.913	8.646	10.301
beta_H[7,5]	6.759	0.347	6.097	6.747	7.466
beta_H[8,5]	8.214	0.213	7.847	8.200	8.637
beta_H[9,5]	8.200	0.484	7.252	8.212	9.169
beta_H[10,5]	10.089	0.228	9.631	10.089	10.556
beta_H[11,5]	11.513	0.230	11.052	11.514	11.955
beta_H[12,5]	8.484	0.198	8.098	8.483	8.887
beta_H[13,5]	10.010	0.131	9.758	10.006	10.269
beta_H[14,5]	9.203	0.232	8.770	9.186	9.693
beta_H[15,5]	11.165	0.239	10.689	11.165	11.635
beta_H[16,5]	9.915	0.180	9.542	9.923	10.246
beta_H[1,6]	10.186	0.187	9.864	10.173	10.577
beta_H[2,6]	11.513	0.109	11.302	11.513	11.737
beta_H[3,6]	10.813	0.163	10.474	10.820	11.109
beta_H[4,6]	12.896	0.829	11.228	12.914	14.453
beta_H[5,6]	5.887	0.612	4.720	5.886	7.104
beta_H[6,6]	8.744	0.675	6.989	8.871	9.743
beta_H[7,6]	9.866	0.587	8.680	9.881	11.043
beta_H[8,6]	9.510	0.275	8.987	9.532	9.956
beta_H[9,6]	8.456	0.798	6.926	8.435	10.078
beta_H[10,6]	9.511	0.323	8.797	9.541	10.074
beta_H[11,6]	10.812	0.349	10.089	10.833	11.454
beta_H[12,6]	9.385	0.248	8.918	9.379	9.887
beta_H[13,6]	11.049	0.154	10.763	11.046	11.368
beta_H[14,6]	9.828	0.291	9.248	9.830	10.392
beta_H[15,6]	10.840	0.419	10.021	10.837	11.676
beta_H[16,6]	10.537	0.243	10.035	10.547	10.996
beta_H[1,7]	10.910	0.869	8.814	11.015	12.390
beta_H[2,7]	12.206	0.448	11.284	12.213	13.081
beta_H[3,7]	10.550	0.658	9.100	10.604	11.633
beta_H[4,7]	2.502	4.202	-5.520	2.407	10.697
beta_H[5,7]	6.465	1.817	3.044	6.401	10.715
beta_H[6,7]	9.626	2.438	4.698	9.554	15.870
beta_H[7,7]	10.540	2.901	4.711	10.505	16.293
beta_H[8,7]	10.968	1.022	9.497	10.904	12.688
beta_H[9,7]	4.463	4.040	-3.619	4.539	12.056
beta_H[10,7]	9.827	1.466	7.200	9.719	13.054
beta_H[11,7]	10.959	1.683	7.884	10.841	14.494
beta_H[12,7]	10.003	0.931	7.963	10.089	11.606
beta_H[13,7]	11.664	0.719	9.950	11.751	12.792
beta_H[14,7]	10.415	0.929	8.433	10.470	12.136
beta_H[15,7]	11.972	2.170	7.782	11.949	16.303
beta_H[16,7]	12.310	1.268	10.190	12.158	15.272
beta0_H[1]	8.840	13.647	-18.381	8.855	36.009
beta0_H[2]	10.704	6.504	-2.050	10.755	23.315
beta0_H[3]	9.812	9.996	-12.188	9.915	29.936
beta0_H[4]	3.578	185.730	-361.077	4.411	374.162
beta0_H[5]	4.113	23.998	-45.168	4.305	51.173
beta0_H[6]	8.665	51.775	-109.640	7.792	123.020
beta0_H[7]	3.387	133.298	-265.561	5.707	276.493
beta0_H[8]	6.061	41.673	-15.690	6.497	27.562
beta0_H[9]	10.247	125.714	-244.323	10.799	267.623
beta0_H[10]	9.256	34.625	-60.969	9.037	77.914
beta0_H[11]	9.088	49.794	-95.246	8.855	117.562
beta0_H[12]	6.762	11.673	-16.115	6.776	29.663
beta0_H[13]	9.613	10.737	-10.033	9.666	29.881
beta0_H[14]	6.880	12.943	-19.566	7.090	31.297
beta0_H[15]	7.735	109.467	-222.950	8.316	231.637
beta0_H[16]	8.548	26.734	-47.033	8.141	62.996